Bayesian Networks, also known as belief networks, are a directed graphical model that represents a set of variables and their conditional dependencies. They are widely used in various fields such as machine learning, artificial intelligence, and decision-making.

Basic Concepts

  • Nodes: Each variable is represented as a node in the network.
  • Edges: Edges represent the conditional dependencies between variables.
  • Conditional Probability Tables (CPTs): CPTs provide the conditional probabilities of each variable given its parents.

Applications

  • Machine Learning: Bayesian Networks are used in various machine learning tasks such as classification, clustering, and prediction.
  • Artificial Intelligence: They are used in expert systems, natural language processing, and robotics.
  • Decision-Making: Bayesian Networks help in making informed decisions by considering various factors and their dependencies.

Example

Here is a simple Bayesian Network representing the relationship between weather, rain, and umbrella usage:

  • Weather: sunny, rainy
  • Rain: true, false
  • Umbrella: true, false

Edges:

  • Weather → Rain
  • Rain → Umbrella

CPTs:

  • P(Rain|Weather=sunny) = 0.1
  • P(Rain|Weather=rainy) = 0.9
  • P(Umbrella|Rain=true) = 0.8
  • P(Umbrella|Rain=false) = 0.2

Further Reading

For more information on Bayesian Networks, you can refer to the following resources:

Bayesian Network Example